OCEAN TEMPEEATUEES 401 



from which we have 



f 2 (y)= MV I e-w cos ( ~ ay A J dy + C x 



j sin A sin a?/ cos A cos ay [ e-w -f O x 

 Za ( ) 



i/y A /o" 



' 2a e " ayc S (oy + A) +(71 (183) 



where C^ is the constant of integration which must have the value 



MV V~2~ 



- cos A in order that / 2 (0) may equal zero. From equa- 



i(t 



tions (176, 177, 179, and 181) it follows that the horizontal and vertical 

 components of the velocity are respectively 



V = f(z)V e- a cos( ^ -ay A) 



W = fM \ =+ [e-coa(-ay \}dy \MV 

 ( V2 J \4 / ) 



(184) 



df(z} ( f /* . \ , cos A ) 



~ ay cos ( - -^- ay A ) dy = V V 



e~ ay cos (ay -f- A) cos A f- 



^ u,z 



Since the horizontal velocity of the surface water is proportional to the 

 wind velocity (pp. 363, 398) it follows from equation (185) that the 

 vertical velocity of the water is also proportional to the wind velocity. 



The differential equation of a stream line is in general -^-equals 



(JLZ 



w 



the slope of the curve equals equals 



( f I" * Y* cosA )d/(z) 



{ / e~ ay cos ( ay A }dy V 5 



dy ( J \4 / V2a ) dz 



._(_._ (*_ _ ay _A[f (2 ) (186 ) 



which can be reduced to the exact differential equation 



df(z) 

 /(*) " 



whose solution is 



e~ av cos f ^ ay A J dy 



j fe-vcos(- ay \\dy- ^4=1 (187) 

 [cos A e-** cos (ay -{- \)]f(z)= C 2 (188) 



